Yes I'm glad that I found this old discussion.
We just had a case that the instructor setup an "upload a single file" type of assignment with both "Allow resubmitting" and "Prevent late submission" set to NO. The instructor did set up a due date for this assignment though. When one student submitted twice (one before the due date, the other after the due date), Moodle ONLY kept the time stamp (for the assignment view) for the 2nd submission so the instructor thought that the student was turning in late and gave him late penalty. The student was so mad and claimed that he did submit the assignment BEFORE the due date. Then we looked into the course "report" (log), and it did show that he uploaded the assignment twice (one before due date the other is not). However, there is no way we can tell whether his first submission was uploaded successfully, and why he wanted to submit the same assignment for the 2nd time (before the teacher started grading). Any thoughts or comments about such scenario? Is the latest Moodle 2.4.x and 2.5.x still behave the same way?? Thanks!